The agency says there were 380,000 such applications, up from 367,000 (a number that has been revised upward; previously, the agency had estimated there were 357,000 claims in the week ended March 31).

Claims had been running at the lowest pace since March and April 2008. At 380,000, the pace is the lowest since June 2008.

The pace is also now back to where claims were running in January of this year.

Bloomberg News says the report is another sign that "the pace of improvement in the labor market is slowing." Last Friday, there was word that only 120,000 jobs were added to payrolls in March.